Timeline for What are the magnitudes of the acceleration of the falling balls B and C relative to A? (Need help with binomial approximation)
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 18, 2021 at 16:12 | comment | added | Michael Seifert | @IlmariKaronen is correct. This approximation would only be valid if the distances from the balls to the center of the Earth ($r_A$, $r_B$, and $r_C$) were much less than 22 meters. | |
| Nov 18, 2021 at 15:56 | comment | added | Ilmari Karonen | Isn't this backwards? The binomial approximation is valid for $x$ close to $0$, but in this case $\frac{r_A}{22\,{\rm m}} \gg 1$. | |
| Nov 18, 2021 at 15:11 | comment | added | Brendan Darrer | @M-B Thanks, I corrected the typo! | |
| S Nov 18, 2021 at 15:01 | history | edited | Brendan Darrer | CC BY-SA 4.0 |
improved answer
|
| S Nov 18, 2021 at 15:01 | history | suggested | Cross | CC BY-SA 4.0 |
Improved formatting
|
| Nov 18, 2021 at 14:04 | review | Suggested edits | |||
| S Nov 18, 2021 at 15:01 | |||||
| Nov 18, 2021 at 12:02 | comment | added | AccidentalTaylorExpansion | To make this approach more general if you have some condition like $r\ll R$ you can rewrite it as $\frac{r}{R}\equiv x\ll 1$. If you have a function $f(r,R)$ that you want to approximate you can replace each $r$ with $xR$ and finally you can Taylor expand in $x$ because $x$ is a small parameter (while taking $R$ constant) | |
| Nov 18, 2021 at 7:51 | comment | added | Mark H | @M-B You are right about $22^2$. | |
| Nov 18, 2021 at 5:13 | comment | added | M-B | Wait, I think there is a typo in your solution. Instead of $\frac{1}{\sqrt{22}}$ shouldn't it be $\frac{1}{22^2}$ ? | |
| Nov 18, 2021 at 3:34 | vote | accept | M-B | ||
| Nov 18, 2021 at 20:26 | |||||
| Nov 18, 2021 at 1:52 | history | edited | Brendan Darrer | CC BY-SA 4.0 |
improved grammar
|
| Nov 18, 2021 at 1:26 | history | edited | Brendan Darrer | CC BY-SA 4.0 |
improved grammar
|
| Nov 18, 2021 at 1:25 | comment | added | M-B | Thank you so much! I can't believe it didn't occur to me to take out the 22m. Kudos | |
| Nov 18, 2021 at 1:23 | vote | accept | M-B | ||
| Nov 18, 2021 at 3:34 | |||||
| Nov 18, 2021 at 1:22 | history | answered | Brendan Darrer | CC BY-SA 4.0 |